Jamming transitions and avalanches in the game of Dots-and-Boxes

Abstract

We study the game of Dots-and-Boxes from a statistical point of view. The early game can be treated as a case of Random Sequential Adsorption, with a jamming transition that marks the beginning of the end-game. We derive set of differential equations to make predictions about the state of the lattice at the transition, and thus about the distribution of avalanches in the end-game.